GENERAL CHEMISTRY 1140

QUANTUM MECHANICS

ORBITALS

 

BOHR'S PLANETARY MODEL OF THE ATOM (1913)

ELECTRONS ORBIT THE NUCLEUS
    LIKE PLANETS ORBIT THE SUN

ONLY CERTAIN ORBITS ARE ALLOWED (QUANTIZED!)

UPON HEATING, ELECTRON GOES TO A HIGHER ENERGY ORBIT

ELECTRON FALLS BACK TO LOWER ENERGY ORBIT AND EMITS ENERGY AS A PHOTON

 

 

BOHR'S ORBIT THEORY ALLOWED ONE TO PREDICT HYDROGEN SPECTRA QUITE WELL. BUT WHY WERE ONLY CERTAIN ORBITS ALLOWED?

DE BROGLIE (1924) SAID ELECTRONS BEHAVE AS STANDING WAVES

THE WAVELENGTH IS RELATED TO QUANTUM NUMBER n AND THE RADIUS r

AND FURTHER PROPOSED WAVELENGTH RELATED TO MASS, VELOCITY, AND PLANCK'S CONSTANT

A FEW YEARS LATER IT WAS DEMONSTRATED THAT ELECTRONS ARE DIFFRACTED BY METAL FOILS MUCH LIKE X-RAYS.

LIGHT IS FOUND TO HAVE WAVE AND MATTER (PHOTON) PROPERTIES

ELECTRONS ARE FOUND TO HAVE MATTER AND WAVE PROPERITES

NEW PHYSICS!!

NOTE: MANY OF THE NEW IDEAS CAME ON THE HEELS OF OTHER NEW IDEAS
 

 

A GREAT MODEL WITH A FEW PROBLEMS

IT WORKS FOR H, He1+, Li2+, BUT VERY FEW OTHER SPECIES!

    IT APPEARS TO ONLY DESCRIBE THE INTERACTION BETWEEN ONE ELECTRON AND A POSITIVE NUCLEUS

    IT DOES NOT WORK FOR TWO OR MORE ELECTRONS!

IT IMPLIES THAT WE KNOW THE "POSITION" OF A WAVE

IT VIOLATES HEISENBERG'S UNCERTAINTY PRINCIPLE

    HEISENBERG - IT IS IMPOSSIBLE TO KNOW SIMULTANEOUSLY BOTH THE MOMENTUM (p = m v) AND THE POSITION OF A PARTICLE WITH CERTAINTY.

HEISENBERG'S UNCERTAINTY PRINCIPLE (PARAPHRASED)

    IF WE KNOW WHERE IT'S AT, WE DON'T KNOW WHERE IT IS GOING.

    IF WE KNOW WHERE IT'S GOING, WE DON'T KNOW WHERE IT'S AT.

BOHR'S MODEL SAYS WE KNOW BOTH - A VIOLATION

 

SCHRODINGER'S MODEL OF THE ATOM (1926)

FORMULATED AN EQUATION WHICH DESCRIBES THE PARTICLE AND WAVE PROPERTIES OF AN ELECTRON

    WAVE FUNCTION Y HAS NO PHYSICAL MEANING

    BUT Y2 GIVES THE PROBABILITY OF FINDING AN ELECTRON IN THE SPACE DEFINED

    SOLVE Y2 FOR WHOLE UNIVERSE AND THE PROBABILITY OF FINDING THE ELECTRON IS 1 (USELESS CALCULATION)

    SOLVE Y2 SO THAT THE PROBABILITY OF FINDING THE ELECTRON IS 0.9 (90%) AND CALL THIS VOLUME AN "ORBITAL".

    TWO DEFINITIONS

      AN ORBITAL IS A REGION IN SPACE WHERE THE PROBABILITY OF FINDING THE ELECTRON IN QUESTION IS HIGH (90%)

      AN ORBITAL IS A REGION IN SPACE WHERE THE ELECTRON WAVE DENSITY IS HIGH (90%)

CAN BE SOLVED FOR THE H ATOM AND OTHER ONE ELECTRON IONS

CAN'T BE SOLVED EXACTLY FOR 2+ ELECTRON SYSTEMS

CAN BE SOLVED APPROXIMATELY FOR 2+ ELECTRON SYSTEMS

    GIVES RESULTS CONSISTANT WITH OBSERVATIONS SO WE WILL USE IT!

TO DESCRIBE THE ORBITALS NEED THREE QUANTUM NUMBERS AND THEIR SELECTION RULES

 

n = PRINICIPAL QUANTUM NUMBER

n = 1, 2, 3, 4, 5.... (INTEGER VALUES)

SAME n AS IN BOHR'S EQUATION

n RELATES TO RELATIVE ENERGIES AS WELL AS THE SIZE OF THE ORBITAL

    ORBITAL WITH n = 3 IS HIGHER IN ENERGY THAN n = 2

    ORBITAL WITH n = 3 IS LARGER THAN n = 2

 

l = ANGULAR MOMENTUM QUANTUM NUMBER

l = 0, 1, .... (n - 2), (n - 1) (INTEGER VALUES)

l DESCRIBES THE SHAPE OF THE ORBITAL

    DIFFFERENT VALUES OF l HAVE DIFFERENT NAMES

      l    NAME

      0      s
      1      p
      2      d
      3      f
      4      g
      5      h

        LETTER DESIGNATIONS CAME OUT OF EARLY SPECTROSCOPY

ALL ORBITALS WITH THE SAME n ARE SAID TO BE IN THE SAME "SHELL"

    3s, 3p, 3d

 

ALL ORBITALS WITH THE SAME n AND l ARE SAID TO BE IN THE SAME "SUBSHELL"

    THE THREE 2p ORBITALS

 

ml = MAGNETIC QUANTUM NUMBER

ml = -l, (-l +1), ... 0 ...(l - 1), +l (INTEGER VALUES)

ml DESCRIBES ORIENTATION IN SPACE

    x LIES ON THE x AXIS
      px, py, pz

    xy IS BETWEEN THE x AND y AXES, ETC.
      dxy, dxz, dyx, dx2 - y2, dz2

 

THESE THREE QUANTUM NUMBERS DESCRIBE SPECIFIC ORBITALS

n   l   ml  ORBITAL NAME

1   0   0   1s
2   0   0   2s
2   1  -1   2px
2   1   0   2py
2   1 +1   2pz
3   0   0   3s
3   1  -1   3px
3   1   0   3py
3   1 +1   3pz
3   2  -2   3dxy
3   2  -1   3dxz
3   2   0   3dyz
3   2 +1   3dz2
3   2 +2   3dx2 - y2
4   0   0   4s
 

WHAT ARE THE SHAPES OF THE ORBITALS?

1s

1s

2px

2py

2pz

ALL THREE 2p ORBITALS

3dz2

3dxz

3dxy

 

THE IMAGES ABOVE COME FROM THE SITES BELOW AND THE INDIVIDUALS INVOLVED DESERVE A LOT OF CREDIT. BY VIEWING THESE SITES YOU CAN ALSO SEE HOW DIFFERENT INDIVIDUALS PORTRAY ORBITALS IN DIFFERENT FORMATS. SOMETIMES A PARTICULAR SITE MIGHT BE VERY SLOW. BY LINKING THE ABOVE IMAGES HERE, WE ARE MINIMIZING TRAFFIC AT THEIR SITES.

 

 

THE FOURTH QUANTUM NUMBER IS ASSOCIATED WITH SPECIFIC ELECTRONS

ms = SPIN QUANTUM NUMBER

ms = -1/2, +1/2

    ELECTRONS BEHAVE LIKE MAGNETS
      CAUSED BY SPINNING CHARGE
    HAVE TWO ORIENTATIONS IN A MAGNETIC FIELD

EACH UNIQUE SET OF FOUR QUANTUM NUMBERS DESCRIBES A UNIQUE ELECTRON IN A GIVEN ATOM

 

ORBITAL ENERGIES

 

WHAT DETERMINES ENERGY OF AN ELECTRON?

1. THE ORBITAL THAT THE ELECTRON IS IN.

 

 

2. THE CHARGE ON THE NUCLEUS

 

 

3. OTHER ELECTRONS IN THE ATOM

    ELECTRONS BETWEEN NUCLEUS AND ELECTRON WE ARE EXAMINING "SHIELD" THE NUCLEUS
      THAT IS, THE ELECTRON EXPERIENCES A SMALLER "EFFECTIVE NUCLEAR CHARGE (Zeff)

 

 

NOW LET'S CONSIDER ALL ORBITALS

 

 

REMINDER: IF THERE IS ONLY ONE ELECTRON, THE 2S AND THE 2p ORBITALS HAVE IDENTICAL ENERGIES, AND THE 3s, 3p, AND 3d ORBITALS HAVE IDENTICAL ENERGIES!
 

 

ANOTHER REPRESENTATION

 

FROM WebElements

 

REMEMBER: THE 2p ORBITAL IN HIGHER IN ENERGY THAN THE 2s ORBITAL IN THE MULTI-ELECTRON ATOM?

2s ORBITAL IS CLOSER TO NUCLEUS THAN 2p ORBITAL
2s ELECTRON IS NOT "SHIELDED" AS MUCH BY THE 1s ELECTRON

CONSEQUENCES:

2s ELECTRON IS HELD MORE TIGHTLY THAN 2p
OR IT TAKES MORE ENERGY TO REMOVE 2s ELECTRON THAN 2p

 

HOW CAN ONE KEEP ORBITAL ENERGIES STRAIGHT?

 

 

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